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Register a new userResonant states in an attractive one dimensional cusp potential
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We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric attractive cusp potential. The components of the spinor solution are expressed in terms of Whittaker functions. We compute the bound states solutions and show that, as the potential amplitude increases, the lowest energy state sinks into the Dirac sea becoming a resonance. We characterize and compute the lifetime of the resonant state with the help of the phase shift and the Breit-Wigner relation. We discuss the limit when the cusp potential reduces to a delta point interaction.
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We derive the nucleon-nucleon isoscalar spin-orbit potential from the Skyrme model and find good agreement with the Paris potential. This solves a problem that has been open for more than thirty years and gives a new geometric understanding of the spin-orbit force. Our calculation is based on the dipole approximation to skyrmion dynamics and higher order perturbation theory.
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We investigate the response to radio-frequency driving of an ultracold gas of attractively interacting fermions in a one-dimensional optical lattice. We study the system dynamics by monitoring the driving-induced population transfer to a third state, and the evolution of the momentum density and pair distributions. Depending on the frequency of the radio-frequency field, two different dynamical regimes emerge when considering the evolution of the third level population. One regime exhibits (off)resonant many-body oscillations reminiscent of Rabi oscillations in a discrete two-level system, while the other displays a strong linear rise. Within this second regime, we connect, via linear response theory, the extracted transfer rate to the system single-particle spectral function, and infer the nature of the excitations from Bethe ansatz calculations. In addition, we show that this radio-frequency technique can be employed to gain insights into this many-body system coupling mechanism away from equilibrium. This is done by monitoring the momentum density redistributions and the evolution of the pair correlations during the drive. Capturing such non-equilibrium physics goes beyond a linear response treatment, and is achieved here by conducting time-dependent matrix product state simulations.
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